TY - JOUR
T1 - On the existence of stable, causal multipliers for systems with slope-restricted nonlinearities
AU - Turner, Matthew
AU - Kerr, Murray
AU - Postlethwaite, Ian
PY - 2009/10
Y1 - 2009/10
N2 - The stability of a feedback interconnection of a linear time invariant (LTI) system and a slope-restricted nonlinearity is revisited. Unlike the normal treatment of this problem, in which multipliers are explicitly chosen and then stability conditions checked, this technical note derives existence conditions for a sub-class of these multipliers, namely those which are L 1 bounded, stable, causal and of order equal to the LTI part of the system. It is proved that for the single-input-single-output case, these existence conditions can be expressed as a set of linear matrix inequalities and thus can be solved efficiently with modern optimization software. Examples illustrate the effectiveness of the results.
AB - The stability of a feedback interconnection of a linear time invariant (LTI) system and a slope-restricted nonlinearity is revisited. Unlike the normal treatment of this problem, in which multipliers are explicitly chosen and then stability conditions checked, this technical note derives existence conditions for a sub-class of these multipliers, namely those which are L 1 bounded, stable, causal and of order equal to the LTI part of the system. It is proved that for the single-input-single-output case, these existence conditions can be expressed as a set of linear matrix inequalities and thus can be solved efficiently with modern optimization software. Examples illustrate the effectiveness of the results.
KW - linear time invariant systems
U2 - 10.1109/TAC.2009.2031581
DO - 10.1109/TAC.2009.2031581
M3 - Article
SN - 0018-9286
VL - 54
SP - 2697
EP - 2702
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 11
ER -